Pointwise information

In mathematics, the qualifier pointwise is used to indicate that a certain property is defined by considering each value f ( x ) {\displaystyle f(x)}...

In mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function. It is weaker than...

In mathematics, the pointwise product of two functions is another function, obtained by multiplying the images of the two functions at each value in the...

In statistics, probability theory and information theory, pointwise mutual information (PMI), or point mutual information, is a measure of association...

uniform convergence is a mode of convergence of functions stronger than pointwise convergence. A sequence of functions ( f n ) {\displaystyle (f_{n})} converges...

operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm. The...

{\displaystyle (S,\Sigma ,\mu )} . Suppose that the sequence converges pointwise to a function f {\displaystyle f} and is dominated by some integrable...

functions: the pointwise, pairwise, and listwise approach. In practice, listwise approaches often outperform pairwise approaches and pointwise approaches...

set X into a vector space has a natural vector space structure given by pointwise addition and scalar multiplication. In other scenarios, the function space...

these confidence intervals constitute a 95% pointwise confidence band for f(x). In mathematical terms, a pointwise confidence band f ^ ( x ) ± w ( x ) {\displaystyle...

well. This theorem does not hold if uniform convergence is replaced by pointwise convergence. For example, let ƒn : [0, 1] → R be the sequence of functions...

equicontinuous and converges pointwise to a function (not necessarily continuous a-priori). In particular, the limit of an equicontinuous pointwise convergent sequence...

called pointwise limit, denoted x n , m → y m pointwise {\displaystyle x_{n,m}\to y_{m}\quad {\text{pointwise}}} , or lim n → ∞ x n , m = y m pointwise {\displaystyle...

(see microcontinuity). The formal definition and the distinction between pointwise continuity and uniform continuity were first given by Bolzano in the 1830s...

In mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a vast number...

turned into a vector space under the operations of pointwise addition of functions and pointwise scalar multiplication. All sequence spaces are linear...

the function; but if the function is analytic then the series converges pointwise to the function, and uniformly on every compact subset of the convergence...

{\displaystyle h_{\nu }=-\nabla \cdot \mathbf {F} _{\nu }} . They define (pointwise) monochromatic radiative equilibrium by ∇ ⋅ F ν = 0 {\displaystyle \nabla...

Non-UI sequence of RVs. The area under the strip is always equal to 1, but X n → 0 {\displaystyle X_{n}\to 0} pointwise....

In mathematics, the lower envelope or pointwise minimum of a finite set of functions is the pointwise minimum of the functions, the function whose value...

a group of loops in a topological group G with multiplication defined pointwise. In its most general form a loop group is a group of continuous mappings...

the sequence of corresponding characteristic functions {φn} converges pointwise to the characteristic function φ of X. Convergence in distribution is...

to occur. Determination of convergence requires the comprehension of pointwise convergence, uniform convergence, absolute convergence, Lp spaces, summability...

{\displaystyle R[n],} n ∈ Z , {\displaystyle n\in \mathbb {Z} ,} The pointwise product: h P ( x ) ≜ s P ( x ) ⋅ r P ( x ) {\displaystyle h_{_{P}}(x)\triangleq...

{p(x,y)}{p(x)\,p(y)}}} where SI (Specific mutual Information) is the pointwise mutual information. A basic property of the mutual information is that...

define pointwise Cauchy convergence, uniform convergence, and uniform Cauchy convergence of the sequence. Pointwise convergence implies pointwise Cauchy-convergence...